In an image, a particular pixel can be represented in a RGB color space as follows:R(x,y)=∫I(x,y,z)×CR(λ)dλG(x,y)=∫I(x,y,z)×CG(λ)dλB(x,y)=∫f(x,y,z)×CB(λ)dλ  (1)where R, G and B represent pixel values of the pixel, x and y represent horizontal and vertical position values of the pixel, and CR(λ), CG(λ), and CB(λ) represent transmission responses of R, G, B color filters in an image-capturing device (e.g., a camera).
Lens shading effects often occur in an image-capturing device (e.g., a camera). One common lens shading effect involves color non-uniformity in an image. That is, a same color in reality becomes different colors at a center of a captured image and at a corner of the captured image. The color lens shading effect is often caused by, for example, optical cross-talk, defective infrared filter, etc.
Considering the color lens shading (CLS) effects, the pixel values of the pixel can be determined as follows:R(x,y)=∫I(x,y,z)×CR(λ)×CLS(λ,α(x,y))dλG(x,y)=∫I(x,y,z)×CG(λ)×CLS(λ,α(x,y))dλB(x,y)=∫I(x,y,z)×CB(λ)×CLS(λ,α(x,y))dλ  (1)where CLS(λ, α(x, y)) represents a CLS gain function, and a represents an incident angle that is a function of pixel position.
A CLS gain is determined as follows:
                                          Gain            X                    ⁡                      (                          x              ,              y                        )                          =                              ∫                                                            I                  ⁡                                      (                                          x                      ,                      y                      ,                      λ                                        )                                                  ⨯                                                      C                    X                                    ⁡                                      (                    λ                    )                                                  ⨯                                  CLS                  ⁡                                      (                                          λ                      ,                                              α                        ⁡                                                  (                                                      x                            ,                            y                                                    )                                                                                      )                                                              ·                              ⅆ                λ                                                          ∫                                                            I                  ⁡                                      (                                          x                      ,                      y                      ,                      λ                                        )                                                  ⨯                                                      C                    X                                    ⁡                                      (                    λ                    )                                                              ·                              ⅆ                λ                                                                        (        2        )            where X represents a R channel, a G channel, or a B channel.